Normalizing Flows

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Normalizing flows learn reversible transformations from a simple distribution, such as a Gaussian, into a complex one, allowing both samples and exact probability densities to be computed. Common approaches include coupling and autoregressive layers, spline transformations, continuous flows, and structured or conditional flows for tasks such as image generation, Bayesian inference, anomaly detection, and control. Current work also combines flows with compact latent representations, flow matching, and physics-informed models, extending their use in scientific simulation and uncertainty estimation. A central tension is balancing expressive, multimodal models against efficient and stable computation, while ensuring that good likelihoods translate into reliable mode coverage and calibrated uncertainty.

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73 papers7 papers in the last four weeks, down 12% on the four weeks before. 0.0% of all new papers.

Learning Normal Coordinates on Riemannian Manifolds with Flow Charts
Oct 20, 2026Edmond CunninghamRiemannian Geometry Normalizing Flows
University of Massachusetts Amherst
Normalizing Flow Maps
Oct 15, 2026Francesco M. Ruscio, Timothy James Hitge, Fred Zhangzhi Peng +6Normalizing Flows Flow Map Learning
AITHYRA · Imperial College London · TU Wien +5
The Blume-Capel Model as a $φ^6$ Field Theory: A Monte Carlo and Flow Model Study
Oct 14, 2026Ejaaz Merali, Ryan Larson, Ehsan Khatami +1Phase Transitions Normalizing Flows
Department of Physics and Astronomy, University of California, Davis, CA 95616, USA · Department of Physics and Astronomy, San José State University, San José, CA 95192 USA
Ergodic topology sampling toward the continuum with Stochastic Normalizing Flows
Oct 14, 2026Claudio Bonanno, Andrea Bulgarelli, Elia Cellini +4Lattice Field Theory High-Energy Physics
Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstraße 5, CH-3012 Bern, Switzerland · Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter) and Helmholtz Institute for Radiation and Nuclear Physics (HISKP), University of Bonn, Nussallee 14-16, 53115 Bonn, Germany · Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom +3
NFMap: Topographic 2D Manifold Learning with Invertible Normalizing Flows
Oct 12, 2026Héléna Alexandra GasparDimensionality Reduction Manifold Learning
LovingScience 124 City Road, London EC1V 2NX
A perspective note on likelihood approximation and inference for complex simulation models using a chain of aggregated normalizing flows
Oct 5, 2026Getachew K BefekaduSimulation-Based Inference Surrogate Modeling
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING, COLLEGE OF ENGINEERING, PHYSICS, AND COMPUTING, THE CATHOLIC UNIVERSITY OF AMERICA, WASHINGTON, DC 20064, USA.
Learning Causal Normalizing Flows from Incomplete Data via Observed-Data Likelihood
Sep 29, 2026Trung-Dung Hoang, Alceu Bissoto, Tim Flühmann +4Normalizing Flows Learning with Missing Data
Department of Digital Medicine, University of Bern, Switzerland · Department of Diabetes, Endocrinology, Nutritional Medicine and Metabolism (UDEM), Inselspital, Bern University Hospital, University of Bern, Switzerland · Graduate School for Cellular and Biomedical Sciences (GCB), University of Bern, Switzerland +3
SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows
Sep 26, 2026Vikas KanaujiaLattice Field Theory Sampling from Unnormalized Distributions
Mahindra University Department of Electrical and Computer Engineering Hyderabad, Telangana, India
Bridging Stochastic Flow Maps and Boltzmann Generators with Normalizing Flows
Sep 25, 2026Louis Grenioux, RuiKang OuYang, Luhuan WuBoltzmann Sampling Molecular Generation
Center for Computational Mathematics, Flatiron Institute, New York, NY, USA · Department of Engineering, University of Cambridge, Cambridge, UK · Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA
Riemannian Neural Hamiltonian Flows: Geodesic Symplectic Transport and Interpretability
Sep 18, 2026Vincent SouvetonNormalizing Flows Hamiltonian Dynamics
CEA, DAM, DIF, Arpajon, F-91297, France
Likelihood-free inference with nuisance parameters through normalizing flows
Sep 9, 2026Phil AsshetonSimulation-Based Inference Normalizing Flows
statsadvice.com, Berlin, Germany.
Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation
Sep 8, 2026Qi Feng, Rongjie Lai, Di Qi +1Normalizing Flows Molecular Generation
Department of Mathematics, Florida State University, Tallahassee, FL 32306 · Department of Mathematics, Purdue University, West Lafayette, IN 47907
$α$ -Graph: Attention-Infused Normalizing Flow Approach to Tractable Graph Modeling
Sep 7, 2026Thanh-Dat Truong, Sarah Alharbi, Susan Gauch +3Normalizing Flows Graph Representation Learning
CVIU Lab, Dep. of EECS University of Arkansas · Dep. of Electrical and Computer Engineering Carnegie Mellon University · Dep. of EECS2026 University of Arkansas +1
Learning Informative Prior with Infinite-Dimensional Continuous Normalizing Flow for Bayesian Inverse Problem
Sep 3, 2026Yang Zhao, Junxiong Jia, Tao ZhouNormalizing Flows Bayesian Inverse Problems
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China · Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100190, China
Generative Nested Sampling of Atomistic Thermodynamic Landscapes
Sep 2, 2026Alessandro Coretti, Nico Unglert, Sebastian Falkner +2Normalizing Flows Flow-Based Generative Modeling
Institute of Materials Chemistry, TU Wien, 1060 Vienna, Austria · Institute of Physics, University of Augsburg, 86159 Augsburg, Germany
sRGB Real Noise Modeling via Noise-Aware Sampling with Normalizing Flows
Aug 29, 2026Dongjin Kim, Donggoo Jung, Sungyong Baik +1Image Denoising Normalizing Flows
Dept. of Computer Science, Hanyang University · Dept. of Artificial Intelligence, Hanyang University · Dept. of Data Science, Hanyang University
GuidedFlow: An Attention-Guided Framework for Anomaly Detection in Additive Manufacturing
Aug 24, 2026Sosmita Paul, Krishna RoySpatio-Temporal Attention Anomaly Localization
New Mexico Institute of Mining and Technology Socorro, NM 87801
Fine-tuned Normalizing Flows for ALICE Zero Degree Calorimeter Fast Simulation
Aug 13, 2026Emilia Majerz, Jacek Otwinowski, Witold Dzwinel +1Neural Surrogate Modeling Normalizing Flows
AGH University of Krakow, Poland · The Henryk Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences
NAE: Normalizing AutoEncoder
Aug 12, 2026Muhammad Abdur Rafae, Niels LandwehrNormalizing Flows Autoencoders
University of Hildeshiem
Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
Aug 11, 2026Kiran Madhusudhanan, Christian Klötergens, Lars Schmidt-Thieme +1Long-Term Time Series Forecasting Normalizing Flows
Institute of Computer Science University of Hildesheim Hildesheim, Germany
You Only Flow Once: Calibrated and Real-Time Radar Pose Estimation with Multi-Hypothesis Normalizing Flows
Aug 10, 2026Jonas Leo Mueller, Sebastian Hoefler, Dario Zanca +3Normalizing Flows Millimeter-Wave Radar
Department Artificial Intelligence in Biomedical Engineering (AIBE), Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Munich Center for Machine Learning (MCML), Munich, Germany · Chair of AI-supported Therapy Decisions, LMU München +1
Flow-based conditional cardiac anatomy generation for virtual cohorts
Aug 10, 2026Konstantinos Kevopoulos, Beatrice Moscoloni, Benjamin Alheit +4Normalizing Flows 3D Medical Imaging
Dept. BioMechanical Engineering, Delft University of Technology, Delft, The Netherlands · Division of Cardiovascular Medicine, Hospital of the University of Pennsylvania, Philadelphia, PA, USA · BioMMeda – Institute for Biomedical Engineering and Technology, Ghent University, Ghent, Belgium +2
Leveraging generative models to assist Monte Carlo sampling
Aug 7, 2026Marylou GabriéNormalizing Flows Generative Modeling
Laboratoire de Physique Statistique, École normale supérieure, PSL Research University, 24 rue Lhomond, 75005 Paris, France
Normalizing Flows to Reconstruct Pseudo-PDFs
Jul 28, 2026Yamil Cahuana Medrano, Kostas OrginosNormalizing Flows Bayesian Inverse Problems
Department of Physics William & Mary Williamsburg, VA 23185
Decafs: Disentangled Conditional adversarial Flows
Jul 21, 2026Anirudh jain, Sakshi Varshney, Samuel Kaski +1Disentangled Representation Learning Normalizing Flows
Orion Pharma · Aalto University, Finland · Aalto University +3
PAKE: Learning Whole-Body Loco-Manipulation with Partial Kinematic Embeddings
Jul 13, 2026Zhengmao He, Moonkyu Jung, Hyeongjun Kim +4Normalizing Flows Whole-Body Robotic Manipulation
The Hong Kong University of Science and Technology (Guangzhou). · Korea Advanced Institute of Science and Technology. · ETH Zurich. +1
NFTR: From Provable Mode-Averaging to Geodesic Subgoal Selection in Offline Goal-Conditioned RL
Jul 8, 2026Erdemt Bao, Xing Lei, Jun Chen +2Normalizing Flows Hierarchical RL
Huazhong University of Science and Technology · Xi’an Jiaotong University · University of Electronic Science and Technology of China
Stable Global Weighting of Flow Mixtures using Simplex Exponential Moving Average
Jul 4, 2026Benjamin Wiriyapong, Oktay Karakus, Can Eyupoglu +1Normalizing Flows Mixture-of-Experts Inference
School of Computer Science and Informatics, Cardiff University, Abacws, Cardiff, CF24 4AG, U.K. · Department of Computer Engineering, Turkish Air Force Academy, National Defence University, Istanbul, Türkiye.
Self-conditioned Flow Map Language Models via Fixed-point Flows
Jul 1, 2026Jaehoon Yoo, Wonjung Kim, Floor Eijkelboom +4Normalizing Flows One-Step Generative Modeling
KAIST · University of Amsterdam · Carnegie Mellon University
Physics-informed Conditional Normalizing Flows for Angles-only Cislunar Orbit Determination
Jun 29, 2026Walther Litteri, Massimiliano VasileNormalizing Flows Conditional Distribution Estimation
Aerospace Centre of Excellence, University of Strathclyde, G11XQ Glasgow, UK · Aerospace Centre of Excellence, University of Strathclyde, G1 1XQ Glasgow, UK

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Learning Normal Coordinates on Riemannian Manifolds with Flow Charts

Edmond Cunningham

University of Massachusetts Amherst

Riemannian Geometry Normalizing Flows

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Riemannian manifolds are powerful models for problems with non-Euclidean structure. Recent work in geometric machine learning has focused on training deep neural networks to learn Riemannian metrics from high-dimensional data. However, many geometric algorithms require repeated evaluations of the exponential and logarithmic maps, whose high computational cost restricts the utility of learned Riemannian manifolds in practice. We propose to address this cost by training a conditional invertible neural network, called a flow chart, to approximate normal coordinates around points on a given Riemannian manifold. With this approach, the exponential and logarithmic maps can be approximated by fast Euclidean operations in the model's learned coordinate space. Our main contribution is an efficient loss function for training flow charts that is nonnegative and, under suitable domain assumptions, is zero precisely when the chart is normal. Across sixteen synthetic and data-derived geometries, flow charts are competitive with a specialized neural geodesic interpolator for logarithmic map estimation, while also being able to estimate the exponential map. When pretrained, flow charts provide a median speedup of 60-70x over numerical baselines at comparable logarithmic map estimation error, and their learned coordinates improve the accuracy of a numerical geodesic solver.